Since it can be both, shouldn't Duolingo accept "A modern theater is very interesting"? I've reported it.
I think it was overlooked because we're not native speakers :) To me this sentence sounds really weird somehow.... But I remember you said English is your native language, so I will add this :)
Thank you! Yes, as a native English speaker, I feel the shades of meaning would break down like this:
"Modern theater is very interesting" -> The abstract concept of modern theater is very interesting.
"The modern theater is very interesting" -> Either the abstract concept is interesting, or a specific theater (the building) is interestingly modern.
"A modern theater is very interesting" -> In general, any modern theater (the building) is very interesting.
Thanks for taking your time and explaining that. I know it's a Ukrainian, not an English course, but it's actually very sweet you can help Ukrainians with their English while learning Ukrainian.